This extensive rigorous texbook, developed through instruction at MIT, focuses on nonlinear and other types of iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and the interface between continuous and discrete optimization. Among its special features, the 1) provides extensive coverage of iterative optimization methods within a unifying framework 2) provides a detailed treatment of interior point methods for linear programming 3) covers in depth duality theory from both a variational and a geometrical/convex analysis point of view 4) includes much new material on a number of topics, such as neural network training, discrete-time optimal control, and large-scale optimization 5) includes a large number of examples and exercises detailed solutions of many of which are posted on the internet Much supplementary/support material can be found at the book's web page